Bohr-Type Inequalities for Harmonic Mappings with a Multiple Zero at the Origin

In this paper, we first determine Bohr’s inequality for the class of harmonic mappings \(f=h+\overline{g}\) in unit disk \(\mathbb {D}\), where either both \(h(z)=\sum _{n=0}^{\infty }a_{pn+m}z^{pn+m}\) and \(g(z)=\sum }b_{pn+m}z^{pn+m}\) are analytic bounded or satisfies condition \(|g'(z)|\le d|h'(z)|\) {D}\backslash \{0\}\) some \(d\in [0,1]\) h is bounded. particular, obtain p-symmetric mappings. Also, investigate Bohr-type inequalities with a multiple zero at origin that most results proved to be sharp.